Pseudorandom number generators (PRNGs) are fundamental components in cryptographic algorithms. The new concept of multi-PRNG introduced in this article consists of a unique generator capable of producing multiple streams of pseudorandom numbers. Multiscroll chaotic systems are known for generating multiple scrolls within a single attractor. With the aforementioned this article introduces a novel field-programmable gate array (FPGA) implementation of a multi-PRNG based on a multiscroll chaotic memristive Hopfield neural network (MHNN). The main contribution of this work is the generation of multiple spatially dependent PRNG streams from a chaotic multiscroll system by dividing the phase space of the attractor into sub-phase spaces. Each scroll in the multiscroll attractor functions as an independent PRNG. This innovative approach to generating multiple PRNGs from multiscroll chaotic systems is unprecedented in the existing literature. The 5-D MHNN chaotic model used in this work employs hyperbolic tangent and sine functions, which were implemented through a hardware-efficient CORDIC approach. Besides, The FPGA implementation to produce the chaotic time series leverages the Euler method with 32-bit fixed-point arithmetic, selected for its simplicity and low resource utilization. Finally, The randomness of the binary sequences produced by the multi-PRNG is rigorously validated using the NIST SP 800-22a and TestU01 suites, confirming their potential for cryptographic applications.

This investigation shows the modeling and simulation of the synchronization of two multi-scroll chaotic oscillators in a master-slave topology. The synchronization is performed by Generalized Hamiltonian forms and observer approach from nonlinear control theory. The case of study consists of two 4-scroll attractors based on saturated function series. Finally, the numerical simulation of the synchronization, from the mathematical description, and the circuit implementation using HSPICE models of opamps, show the good agreement between theory and experiment results.

A trade-off analysis on the number of scrolls and the operating frequency is presented. To do so, nonlinear system parameters, real physical active device parameters and the operating frequency are taken into account to model the behavior of the saturated nonlinear function series approximated by a piecewise-linear description. As a consequence, not only the trade-off between the number of scrolls and the operating frequency is investigated, which depends directly on the behavior at the operating frequency of the nonlinear function, but also chaotic attractors are efficiently synthesized without the application of scaling techniques. Theoretical calculations are in good agreement with numerical simulations and a prediction on the maximum number of scrolls that can be synthesized for a particular frequency is also given.